One system of this kind for directly injecting fuel into the combustion chamber of an internal combustion engine is generally known. A so-called stratified charge operation as a first mode of operation and a so-called homogeneous operation as a second mode of operation are distinguished. The stratified operation is used especially for smaller loads; whereas, the homogeneous operation is utilized for larger loads applied to the engine. In stratified operation, the fuel is injected during the compression phase of the engine into the combustion chamber and there, directly into the vicinity of a spark plug. This has the consequence that no uniform distribution of the fuel in the combustion chamber can take place; instead, the fuel is immediately ignited by the spark plug. The advantage of stratified operation lies in that applied lower loads can be carried by the engine with a very small quantity of fuel. Larger loads can, however, not be satisfied with stratified operation. In homogeneous operation, which is provided for such larger loads, the fuel is injected during the induction phase of the engine so that a swirling and therefore a distribution of the fuel in the combustion chamber can still easily take place. Insofar, the homogeneous operation corresponds approximately to the operation of internal combustion engines wherein fuel is injected into the intake manifold in a conventional manner.